Problem: Rewrite as a simplified fraction. ${3.2\overline{4} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 324.4444...\\ 10x &= 32.4444...\end{aligned}}$ Subtracting the two equations, we have: ${90x = 292}$ ${x = \dfrac{292}{90}} $ ${x = \dfrac{146}{45}} \text{or} {3 \dfrac{11}{45}}$